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An ideal gas takes part in two thermal p...


An ideal gas takes part in two thermal process in which it is heated from same initial state A. Once it is taken from A to B and in the other case from A to C. The points B and C lie on an isotherm. Choose the correct options.

A

Change in internal energy for both the process is the same.

B

the heat supplied to gas in `A to B` is greater than that in `A to C`.

C

The heat supplied to gas in `A to B` is less than that is `A to C`.

D

The work done by the gas in `A to B` is equal to than that in `A to C`

Text Solution

Verified by Experts

The correct Answer is:
A, C

`W=`Area of trapezium
`=(1)/(2)(P_(0)+(C)/(V))(V-V_(0))`
`(dW)/(dV)=(1)/(2)(P_(0)+(C)/(V)+(1)/(2)(V-V_(0))(-(C)/(V^(2)))`
`(1)/(2)(P_(0)+(C)/(V)-(C)/(V_(2))(V-V_(0)))`
`=(1)/(2)(P_(0)+(C)/(V)-(C)/(V)+(CV_(0))/(V^(2)))=(P_(0)+(CV_(0))/(V^(2)))`
Since `(dW)/(dV)` is always positive,
Now, work done in process AC is greater than that of AB.
Hence heat supplied in process AC will be more than that of AB.
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