New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Heat and Thermodynamics question

2009 · Shift 0 · Q70

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Heat and Thermodynamics
2009 · Shift 0 · Q70

Heat and Thermodynamics question

2009 · Shift 0 · Q70

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1

One

kg

of a diatomic gas is at a pressure of

8 \times {10^4}\,N/{m^2}.

The density of the gas is

4kg/{m^3}

. What is the energy of the gas due to its thermal motion ?

A
$5 \times {10^4}\,J$
B
$6 \times {10^4}\,J$
C
$7 \times {10^4}\,J$
D
$3 \times {10^4}\,J$

View written solutionFree

Correct answer: A

Given data

Mass of gas: $m = 1\,\text{kg}$
Pressure: $P = 8 \times 10^4\,\text{N/m}^2$
Density: $\rho = 4\,\text{kg/m}^3$

The gas is diatomic, so for ordinary temperatures its degrees of freedom are $f=5$ .

Find the volume of the gas

Using

\rho = \frac{m}{V}

so

V = \frac{m}{\rho} = \frac{1}{4} = 0.25\,\text{m}^3

Use the formula for thermal (internal) energy

For an ideal gas,

U = \frac{f}{2}PV

For a diatomic gas,

U = \frac{5}{2}PV

Now,

PV = (8 \times 10^4)(0.25) = 2 \times 10^4\,\text{J}

Therefore,

U = \frac{5}{2}(2 \times 10^4) = 5 \times 10^4\,\text{J}

Check options

A: $5 \times 10^4\,\text{J}$ ✅
B: $6 \times 10^4\,\text{J}$
C: $7 \times 10^4\,\text{J}$
D: $3 \times 10^4\,\text{J}$

So the correct option is A.

Comparison with stored answer

Stored correct answer = A

Our derived answer also = A, so they agree.

More from Heat and Thermodynamics

Statement - 1: The temperature dependence of resistance is usually given as $R = R_{0} (1 + α Δ t) .$ The resistance of wire changes from $100Ω$ to $150Ω$ when its temperature is increased from $2 7^{\circ} C$ …2009 · MCQ
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…2008 · MCQ
The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m s^{- 1} .$ The speed of sound in helium $(H e)$ at the same temperature will be (assume both gases to be ideal)2008 · MCQ
One end of a thermally insulated rod is kept at a temperature $T_{1}$ and the other at $T_{2}$ . The rod is composed of two sections of length $L_{1}$ and $L_{2}$ and thermal conductivities $K_{1}$ and $K_{2}$ respectively. The temperature… Includes diagram2007 · MCQ
When a system is taken from state $i$ to state $f$ along the path iaf, it is found that $Q = 50$ cal and $W = 20 c a l$ . Along the path $ib f Q = 36 c a l . W$ along the path $ib f$ is Includes diagram2007 · MCQ
If $C_{p}$ and $C_{v}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then2007 · MCQ
The work of $146 k J$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ} C .$ The gas is $(R = 8.3 J m o l^{- 1} K^{- 1})$ 2006 · MCQ
Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T K$ , evaluate the total radiant powered incident of Earth at a distance $r$ from the Sun Where r0 is the radius of the Earth and $σ$ is Stefan's constant.2006 · MCQ