First Law of Thermodynamics

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JEE Main 2021

LEVELJEE Main

A diatomic gas having $C_{p} = \frac{7}{2} R$ and $C_{V} = \frac{5}{2} R$ , is heated at constant pressure. The ratio $d U : d Q : d W$ is

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $p_{1}$ and temperature $T_{1}$ . The other chamber has volume $V_{2}$ and contains ideal gas at pressure $p_{2}$ and temperature $T_{2}$ . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

(A)

\frac{T _{1} T _{2} ( p _{1} V _{1} + p _{2} V _{2} )}{p _{1} V _{1} T _{2} + p _{2} V _{2} T _{1}}

(B)

\frac{p _{1} V _{1} T _{1} + p _{2} V _{2} T _{2}}{p _{1} V _{1} + p _{2} V _{2}}

(C)

\frac{p _{1} V _{1} T _{2} + p _{2} V _{2} T _{1}}{p _{1} V _{1} + p _{2} V _{2}}

(D)

\frac{T _{1} T _{2} ( p _{1} V _{1} + p _{2} V _{2} )}{p _{1} V _{1} T _{1} + p _{2} V _{2} T _{2}}

JEE Main 2020

LEVELJEE Main

A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to .......

LEVELJEE Main

A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure $p$ and temperature $T$ , whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be

(A)

\frac{p}{2}, \frac{T}{2}

(B)

\frac{p}{2}, T

(C)

p, T

(D)

p, \frac{T}{2}

JEE Main 2019

LEVELJEE Main

Following figure shows two processes A and B for a gas. If $Δ Q_{A}$ and $Δ Q_{B}$ are the amount of heat absorbed by the system in two cases, and $Δ U_{A}$ and $Δ U_{B}$ are changes in internal energies respectively, then

(A)

Δ Q_{A} > Δ Q_{B}, Δ U_{A} > Δ U_{B}

(B)

Δ Q_{A} < Δ Q_{B}, Δ U_{A} < Δ U_{B}

(C)

Δ Q_{A} > Δ Q_{B}, Δ U_{A} = Δ U_{B}

(D)

Δ Q_{A} = Δ Q_{B}, Δ U_{A} = Δ U_{B}

JEE Main 2019

LEVELJEE Main

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is $- 180 J$ . The gas absorbs $250 J$ of heat along the path ab and $60 J$ along the path bc. The work done by the gas along the path abc is

(A)

120 J

(B)

130 J

(C)

100 J

(D)

140 J

JEE Main 2005

LEVELBoard

A system goes from $A$ to $B$ via two processes I and II as shown in figure. If $Δ U_{1}$ and $Δ U_{2}$ are the changes in internal energies in the processes I and II respectively, then

(A)

Δ U_{1} = Δ U_{2}

(B)

relation between

Δ U_{1}

and

Δ U_{2}

cannot be determined

(C)

Δ U_{2} > Δ U_{1}

(D)

Δ U_{2} < Δ U_{1}

JEE Main 2021

LEVELJEE Main

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ} C$ to $5 0^{\circ} C$ when no work is done is ......... . ( $R$ is the universal gas constant)

(A)

250 R

(B)

750 R

(C)

175 R

(D)

500 R

JEE Main 2021

LEVELJEE Main

An electric appliance supplies $6000 J/min$ heat to the system. If the system delivers a power of $90 W$ . How long it would take to increase the internal energy by $2.5 \times 1 0^{3} J$ ?

(A)

2.5 \times 1 0^{2} s

(B)

4.1 \times 1 0^{1} s

(C)

2.4 \times 1 0^{3} s

(D)

2.5 \times 1 0^{1} s

JEE Main 2014

LEVELJEE Main

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K, respectively. Choose the correct statement.

(A)

The change in internal energy in whole cyclic process is

250 R

(B)

The change in internal energy in the process CA is

700 R

(C)

The change in internal energy in the process AB is

- 350 R

(D)

The change in internal energy in the process BC is

- 500 R

LEVELJEE Main

Which of the following is incorrect regarding the first law of thermodynamics?

(A)

It is not applicable to any cyclic process

(B)

It is a restatement of the principle of conservation of energy

(C)

It introduces the concept of the internal energy

Consider a spherical shell of radius $R$ at temperature $T$ . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^{4}$ and pressure $p = \frac{1}{3} (\frac{U}{V})$ . If the shell now undergoes an adiabatic expansion, the relation between $T$ and $R$ is

(A)

T \propto e^{- R}

(B)

T \propto e^{- 3 R}

(C)

T \propto \frac{1}{R}

(D)

T \propto \frac{1}{R ^{3}}

JEE Main 2007

LEVELJEE Main

When a system is taken from state $i$ to state $f$ along the path $ia f$ , it is found that $Q = 50 cal$ and $W = 20 cal$ . Along the path $ib f$ , $Q = 36 cal$ . $W$ along the path $ib f$ is

(A)

6 cal

(B)

16 cal

(C)

66 cal

(D)

14 cal

JEE Main 2021

LEVELJEE Main

1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{x R}{8}$ , The value of $x$ is ........... . $[R = universal gas constant]$

JEE Main 2019

LEVELJEE Main

$n$ moles of an ideal gas with constant volume heat capacity $C_{V}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

(A)

\frac{4 n R}{C _{V} + n R}

(B)

\frac{4 n R}{C _{V} - n R}

(C)

\frac{n R}{C _{V} - n R}

(D)

\frac{n R}{C _{V} + n R}

JEE Main 2019

LEVELJEE Main

A gas can be taken from $A$ to $B$ via two different processes $A C B$ and $A D B$ . When path $A C B$ is used 60 J of heat flows into the system and 30 J of work is done by the system. If path $A D B$ is used work done by the system is 10 J the heat flow into the system in path $A D B$ is

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $γ$ . It is moving with speed $v$ and its suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by

(A)

\frac{( γ - 1 )}{2 γ R} M v^{2} K

(B)

\frac{γ M v ^{2}}{2 R} K

(C)

\frac{( γ - 1 )}{2 R} M v^{2} K

(D)

\frac{( γ - 1 )}{2 ( γ + 1 ) R} M v^{2} K

JEE Main 2021

LEVELJEE Main

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ...... $π$ J.

LEVELJEE Main

100g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K)

A rigid container with thermally insulated walls contains a coil of resistance $100 Ω$ , carrying current $1 A$ . Change in internal energy after $5 min$ will be

(A)

zero

(B)

10 kJ

(C)

20 kJ

(D)

30 kJ

JEE Advanced 2003

LEVELJEE Main

An insulated box containing a monoatomic gas of molar mass $M$ moving with a speed $v_{0}$ is suddenly stopped. Find the increment in gas temperature as a result of stopping the box.

JEE Advanced 2014

LEVELJEE Advanced

A thermodynamic system is taken from an initial state $i$ with internal energy $U_{i} = 100 J$ to the final state $f$ along two different paths $ia f$ and $ib f$ , as schematically shown in the figure. The work done by the system along the paths $a f$ , $ib$ and $b f$ are $W_{a f} = 200 J$ , $W_{ib} = 50 J$ and $W_{b f} = 100 J$ respectively. The heat supplied to the system along the path $ia f$ , $ib$ and $b f$ are $Q_{ia f}$ , $Q_{ib}$ and $Q_{b f}$ respectively. If the internal energy of the system in the state $b$ is $U_{b} = 200 J$ and $Q_{ia f} = 500 J$ , the ratio $Q_{b f} / Q_{ib}$ is

LEVELJEE Main

For an ideal gas

* Multiple Correct Options

(A)

the change in internal energy in a constant pressure process from temperature

T_{1}

T_{2}

is equal to

n C_{V} (T_{2} - T_{1})

, where

C_{V}

is the molar heat capacity at constant volume and

n

the number of moles of the gas

(B)

the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process

(C)

the internal energy does not change in an isothermal process

(D)

no heat is added or removed in an adiabatic process

LEVELJEE Advanced

A sample of $2 kg$ monoatomic helium (assumed ideal) is taken through the process $A B C$ and another sample of $2 kg$ of the same gas is taken through the process $A D C$ (see fig). Given molecular mass of helium = $4$ . (a) What is the temperature of helium in each of the states $A, B, C$ and $D$ ? (b) Is there any way of telling afterwards which sample of helium went through the process $A B C$ and which went through the process $A D C$ ? Write Yes or No. (c) How much is the heat involved in the process $A B C$ and $A D C$ ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A diatomic gas having Cp​=27​R and CV​=25​R, is heated at constant pressure. The ratio dU:dQ:dW is

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to .......

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by 2.5×103 J?

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K, respectively. Choose the correct statement.

Which of the following is incorrect regarding the first law of thermodynamics?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } When a system is taken from state i to state f along the path iaf, it is found that Q=50 cal and W=20 cal. Along the path ibf, Q=36 cal. W along the path ibf is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the reported figure, heat energy absorbed by a system in going through a cyclic process is ...... πJ.

100g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A rigid container with thermally insulated walls contains a coil of resistance 100 Ω, carrying current 1 A. Change in internal energy after 5 min will be

For an ideal gas

A diatomic gas having $C_{p} = \frac{7}{2} R$ and $C_{V} = \frac{5}{2} R$ , is heated at constant pressure. The ratio $d U : d Q : d W$ is

An electric appliance supplies $6000 J/min$ heat to the system. If the system delivers a power of $90 W$ . How long it would take to increase the internal energy by $2.5 \times 1 0^{3} J$ ?

When a system is taken from state $i$ to state $f$ along the path $ia f$ , it is found that $Q = 50 cal$ and $W = 20 cal$ . Along the path $ib f$ , $Q = 36 cal$ . $W$ along the path $ib f$ is

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ...... $π$ J.

A rigid container with thermally insulated walls contains a coil of resistance $100 Ω$ , carrying current $1 A$ . Change in internal energy after $5 min$ will be