Ideal gas heating
The above shows a resistor with resistance
installed in a cylinder filled with a fixed quantity of ideal gas. We connect the resistor to a power supply with a voltage of
to provide heating energy in the cylinder. Suppose the pressure and volume of the ideal gas before and after heating are
and
respectively. If the internal energy of the ideal gas before heating is
then what is the change in the amount of the internal energy
after heating? (The cylinder is sealed completely.)
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Use the ideal gas law PV/T = constant. Assume the initial temperature to be 't' and final temperature to be 'T'. given the necessary information about initial P, V and final P, V, try to express T in terms of t. It comes out to be T= 1.5t, so change in temperature is 0.5t. If initial internal energy associated with temperature t is U, and since internal energy of an ideal gas is proportional to temperature thus change in internal energy energy is 0.5U or U/2.