A piston-cylinder assembly with the piston resting on a set of stops, contains 0.5 Kg of He gas intially at 100kPa and 25C. The mass of the piston and the effect of the atmospheric pressure is such that a pressure of 500kPa is required to raise it. How much energy must be transferred by heat to the He in kJ, before the piston starts rising?
Assume ideal gas
To find the amount of energy that must be transferred by heat to the helium gas before the piston starts rising, we need to calculate its internal energy change.
First, let's establish the initial and final states of the helium gas:
- Initial state: Pressure P1 = 100 kPa, Temperature T1 = 25 °C
- Final state: Pressure P2 = 500 kPa (required to raise the piston)
Step 1: Convert the temperatures to Kelvin
The temperature in Kelvin (T) is obtained by adding 273.15 to the Celsius temperature.
T1 = 25 + 273.15 = 298.15 K
Step 2: Calculate the initial and final volumes
Since the piston is initially resting on a set of stops, the initial volume (V1) is not given. However, we can use the ideal gas law to determine V1:
PV = nRT
V1 = (nRT1) / P1
The final volume (V2) is not explicitly given, but we know that the initial state is at rest and the final state requires a pressure of 500 kPa to raise the piston. This implies that the volume change is only due to the displacement of the piston. The volume change (ΔV) is the difference between the initial and final volumes:
ΔV = V2 - V1
Step 3: Calculate the work done on the gas
The work done on the gas is given by:
W = P2 * ΔV
Step 4: Calculate the change in internal energy
ΔU = Q - W
Since the gas undergoes an isochoric (constant volume) process, the change in internal energy (ΔU) is equal to the heat transferred (Q). Therefore:
Q = ΔU = W
Step 5: Convert the work done into energy in kilojoules.
Since the work is given in joules, we need to convert it to kilojoules by dividing by 1000:
Q (in kJ) = W / 1000
Now you can follow these steps and calculations to find the answer to the question.