8.31 Wh (watthours) heat is transmitted to 1 mole single atomic ideal gas. The gas temperature is 27°C and the pressure is constant during the process (slow process). What is the temperature? What is the change of the internal energy of the gas? What is the work done during the gas is surrounding?

To answer these questions, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

ΔU = Q - W

where:
ΔU = change in internal energy
Q = heat added to the system
W = work done by the system

Let's solve each question step by step:

1. What is the temperature?
To determine the temperature, we need to use the ideal gas law:

PV = nRT

where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since the pressure and number of moles are constant in this case, we can simplify the equation to:

V/T = constant

Therefore, the ratio of volume to temperature is constant. So, if the volume remains constant, then the temperature also remains constant. As a result, the temperature is 27°C.

2. What is the change in the internal energy of the gas?
We can calculate the change in internal energy using the formula mentioned earlier:

ΔU = Q - W

In this case, ΔU represents the change in internal energy, Q is the heat added to the system, and W is the work done by the system. The heat added to the system is given as 8.31 Wh (or 8.31 Joules).

Since the process is slow, the work done by the system is zero (W = 0) because there is no change in volume (as mentioned earlier). Therefore, the change in internal energy (ΔU) is equal to the heat added to the system, which is 8.31 Wh.

3. What is the work done during the process?
Since the pressure is constant and there is no change in volume (V), the work done by the gas is zero (W = 0) in this case. This is because work done by a gas is given by the formula:

W = PΔV

where P is the pressure, and ΔV is the change in volume. Since there is no change in volume, the work done is zero.

To summarize:
- The temperature remains 27°C.
- The change in internal energy (ΔU) is equal to 8.31 Wh (or 8.31 Joules).
- The work done by the gas is zero (W = 0).