One mole of an ideal gas in initial state $A$ undergoes a cyclic process $A B C A$ , as shown in the figure. Its pressure at $A$ is $P_{0}$ . Choose the correct option(s) from the following. [2010]

Question

Smart Achievers · Accepted Answer

(1, 2)

$Process A to B$

$Here, T_{A} = T_{B}$ $∴$ $U_{A} = U_{B}$

$Also P_{0} V_{0} = P_{B} \times 4 V_{0}$

$\Rightarrow P_{B} = \frac{P_{0}}{4}$

$Work done$

$W_{A B} = n R T_{0} \log_{e} (\frac{4 V_{0}}{V_{0}})$

$= P_{0} V_{0} \log_{e} 4$ $[∵ P_{0} V_{0} = n R T_{0}]$

$The process BC is not clear. Therefore no judgement can$ $be made at C regarding P and T .$

Solution

Q.
One mole of an ideal gas in initial state $A$ undergoes a cyclic process $A B C A$ , as shown in the figure. Its pressure at $A$ is $P_{0}$ . Choose the correct option(s) from the following. [2010]

1 Internal energies at A and B are the same.

2 Work done by the gas in process AB is $P_{0} V_{0} \ln 4$

3 Pressure at C is $\frac{P_{0}}{4}$

4 Temperature at C is $\frac{T_{0}}{4}$

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Solution

Q. One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choose the correct option(s) from the following. [2010]

1 Internal energies at A and B are the same.

2 Work done by the gas in process AB is P0V0ln4

3 Pressure at C is P04

4 Temperature at C is T04

Ans. (1, 2) Process A to B Here, TA=TB ∴ UA=UB Also P0V0=PB×4V0 ⇒PB=P04 Work done WAB=nRT0loge(4V0V0) =P0V0loge4 [∵P0V0=nRT0] The process BC is not clear. Therefore no judgement can be made at C regarding P and T.

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Q.
One mole of an ideal gas in initial state $A$ undergoes a cyclic process $A B C A$ , as shown in the figure. Its pressure at $A$ is $P_{0}$ . Choose the correct option(s) from the following. [2010]

2 Work done by the gas in process AB is $P_{0} V_{0} \ln 4$

3 Pressure at C is $\frac{P_{0}}{4}$

4 Temperature at C is $\frac{T_{0}}{4}$