Final answer:
To calculate the work done and heat transferred during the isothermal compression of a gas, use the formula W = P1V1 ln(P2/P1), where P1 and P2 are the initial and final pressures, and V1 is the initial volume. The heat transferred, Q, is equal in magnitude and opposite in sign to the work done.
Step-by-step explanation:
The question pertains to an isothermal compression of a gas and involves calculating the work done and the heat transferred during this process. To solve this problem, the ideal gas law and the first law of thermodynamics are used. Since the process is isothermal, the temperature remains constant and the internal energy change (ΔU) of the gas is zero.
For an isothermal process, the work done (W) is given by:
W = nRT ln(Vf/Vi), where n is the number of moles, R is the ideal gas constant, T is the absolute temperature, Vi is the initial volume, and Vf is the final volume.
In this case, the formula can be rearranged to use pressure instead of volume, as we have the values for initial and final pressure, and volume is constant:
W = P1V1 ln(P2/P1)
The heat (Q) transferred for an isothermal process is equal but opposite to the work done (since ΔU = 0 for an ideal gas in an isothermal process):
Q = -W
By applying these formulas and given values, the student will be able to calculate the work done during the compression and heat transferred.