Assume a gas in a container with one end closed and other end has a piston of mass m fixed with a spring.The gas is then heated ,assume that the container is non-conducting.(Assume vessel to be kept in vertical position and the spring is on top).
I have doubt that since the the piston is connected to the spring the pressure inside the gas varies and temperature also varies because the vessel is non-conducting and volume is also not fixed. Then we can calculate the work done by the gas if during the piston has moved 'd' distance. I can't understand how to begin?
Best Answer
From your question, I am not entirely sure what information you know about the system, so I will make some assumptions below. Hopefully it will help get you started at least.
For a spring, we know that the spring force is $F_{S} = kx$ (Hooke's Law). We also know the definition of work $W = Fd $.
Assuming the piston does not accelerate, the force exerted by the gas is the same as the force exerted by the spring. Assuming that we know the spring constant $k$, and the distance $d$, we can calculate the work done by the gas over a tiny interval $dx$ as $F_{s} \cdot dx$. We get the total work done by the gas by integrating:
$$ \int_{0}^{d} F_{s} \ dx = \int_{0}^{d} kx \ dx = \frac{1}{2}kd^{2}$$