Question

When heat is given to a gas in an isothermal change, the result will be
A. External work done
B. Rise in temperature
C. Increase in internal energy
D. External work done and also rise in temp.

Answer 1

Hint:
An isothermal process is one in which the system's temperature stays constant. This indicates that the change in temperature is zero. So, heat is exchanged continuously between the system and surrounding to maintain the temperature of the system constant. So, the system's overall energy content is constant.


Complete step by step solution:

According to the first law of thermodynamics, the change in internal energy is the function only of temperature.
Hence, \[\vartriangle U = f\left( T \right)\] where T is the temperature, \[\vartriangle U\] is change in internal energy.
If temperature is constant then \[\vartriangle U = 0\].
Now, \[\vartriangle Q = \vartriangle U + W\] here \[\vartriangle Q\]is the net heat transfer and W is network done.
\[ \Rightarrow \vartriangle Q = W\]
Now, let's check out the answers one by one. Our first option is that external work is done. As we solved above the net heat transfer will be equal to work done by the system. So heat given to the system will be positive so does the work done. Similarly we already know that the heat is given isothermally, so there is no chance of rise in temperature and change in internal energy.
Hence option A is the correct option.



Therefore, option (A) is the correct option.



Note:
When a gas is compressed isothermally then heat is rejected from the system. The first law of thermodynamics, the change in internal energy is the function only of temperature. The mathematical expression of laws of thermodynamics is, \[\vartriangle Q = \vartriangle U + W\] here \[\vartriangle Q\]is the net heat transfer and W is network done, \[\vartriangle U\]= change in internal energy. There is no change in internal energy as temperature is constant in isothermal processes.