| A system consists of a cylinder, piston and a spring as shown. The initial volume of the cylinder is 100 l and its pressure is \[100 kPa\] so that it just balances the atmosphere pressure plus the piston weight. In this position, the spring connected to the piston exerts no force on it. Heat is now transferred to the system so as to expand air to double its volume, at which the pressure in the cylinder is \[300 kPa\]. The work done by the system is (in case of a spring \[F=-kx\]): |
 |
A) 200 J
B) \[2\times {{10}^{6}}J\]
C) 20 kJ
D) 2kJ
Correct Answer: C
Solution :
| \[{{P}_{av}}=\frac{{{P}_{i}}+{{P}_{f}}}{2}=\left[ \frac{100+300}{2} \right]\times {{10}^{3}}Pa\] |
| \[=200\times {{10}^{3}}Pa\] and \[\Delta V=100\times {{10}^{-3}}{{m}^{3}}\] |
| \[\therefore W={{P}_{av}}\Delta V=200\times {{10}^{3}}\times 100\times {{10}^{-3}}\] |
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