When the gas is heated at constant pressure, the heat supplied
(a) increases the internal energy of the gas
(b) increases the temperature of the gas
(c) does some external work during expansion
(d) both (a) and (b)
The correct answer and explanation is :
The correct answer is (d) both (a) and (b).
Explanation:
When a gas is heated at constant pressure, several processes occur simultaneously. To understand this scenario, we need to look at the thermodynamic principles involved:
- Increase in Internal Energy of the Gas (Option a):
- Internal energy of a gas refers to the total energy contained within the gas molecules, which includes both kinetic energy (due to molecular motion) and potential energy (due to molecular interactions).
- When heat is added to a gas, its temperature increases. This increase in temperature results in the molecules moving faster, increasing the gas’s kinetic energy, which leads to an increase in the internal energy of the gas.
- This can be understood from the first law of thermodynamics, which states: $$
\Delta U = Q – W
$$ Where:- $\Delta U$ is the change in internal energy,
- $Q$ is the heat supplied to the system,
- $W$ is the work done by the system.
- In this case, as the gas is heated, some of the heat goes into increasing the internal energy of the gas.
- Increase in Temperature of the Gas (Option b):
- Temperature is directly related to the average kinetic energy of the molecules in a gas. As heat is supplied to the gas, the temperature of the gas rises because the kinetic energy of the molecules increases.
- According to the ideal gas law, at constant pressure, the temperature and volume of the gas are directly proportional. If the gas is heated, its temperature increases.
- Work Done by the Gas During Expansion (Option c):
- At constant pressure, when a gas is heated, it expands. The expansion of the gas against the external pressure is a form of work done by the gas. This work is given by: $$
W = P \Delta V
$$ where $P$ is the constant external pressure, and $\Delta V$ is the change in volume of the gas. - While some of the heat supplied contributes to work done during expansion, the work done by the gas is not the only result of the heating process, which is why option (c) is not the complete answer.
Therefore, both increased internal energy (a) and increased temperature (b) occur when the gas is heated at constant pressure. Hence, the correct choice is (d) both (a) and (b).