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Question

A gas under constant pressure of $$4.5\times 10^{5}  Pa$$ when subjected to $$800 \ KJ$$ of heat, changes the volume from $$0.5\ m^{3}to\ 
2.0\ m^{3}$$. The change in the internal energy of the gas:


A
6.75×105J
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B
5.25×105J
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C
3.25×105J
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D
1.25×105J
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Solution

The correct option is D $$1.25\times 10^{5} J$$
Given data,
$$P=4.5\times 10^{5}Pa$$
$$dQ=800kJ$$
$$V_{1}=0.5m^{3}$$
$$V_{2}=2m^{3}$$
$$dW=P(V_{2}-V_{1})=4.5\times10^{5}(2\times0.5)$$
$$=6.75\times 10^{5}J$$
Change in internal energy
 $$dU=dQ-dW$$
$$U=800\times 10^3-675\times 10^3$$
$$=125\times 10^3J$$
$$=1.25\times 10^5 J$$
Option D.

Physics

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