IIT-JEE 2008 · Paper 2 · Physics Q44

PhysicsMatrix match+6Question 44 of 66

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I

A
An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened.
B
An ideal monoatomic gas expands to twice its original volume such that its pressure $P\propto\dfrac1{V^2}$ , where $V$ is the volume of the gas
C
An ideal monoatomic gas expands to twice its original volume such that its pressure $P\propto\dfrac1{V^{4/3}}$ , where $V$ is its volume
D
An ideal monoatomic gas expands such that its pressure $P$ and volume $V$ follows the behaviour shown in the graph

Column II

P
The temperature of the gas decreases
Q
The temperature of the gas increases or remains constant
R
The gas loses heat
S
The gas gains heat

Answer and worked solution

Official answer: A → Q; B → P, R; C → P, S; D → Q, S

A, free expansion into vacuum. No heat ( $q=0$ ) and no work, so $\Delta U=0$ and the temperature of an ideal gas stays the same. → Q.
B, $PV^2$ constant. $T\propto PV\propto\frac1V$ : the gas cools. For the polytropic index $n=2$ , the molar heat capacity is $C=C_V+\frac R{1-n}=\frac32R-R=\frac R2>0$ , and with $\Delta T<0$ the gas loses heat. → P, R.
C, $PV^{4/3}$ constant. $T\propto V^{-1/3}$ : cools. Here $C=\frac32R+\frac R{1-4/3}=-\frac32R<0$ , so with $\Delta T<0$ the gas gains heat. → P, S.
D, P and V both increase. $T\propto PV$ rises, and $W>0$ , $\Delta U>0$ , so $q=\Delta U+W>0$ . → Q, S.

Answer: A → Q; B → P, R; C → P, S; D → Q, S

Topics:Thermodynamic processes First law and internal energy Specific heats of gases

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IIT-JEE 2008 · Paper 2, Physics question 44