An ideal gas was slowly compressed at constant temperature to one-half it’s original volume. In the process, 150 kcal of heat was given off. How much work was done by the gas (in joules)?
To determine the work done by the gas, we can 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.
Mathematically, this can be expressed as:
ΔU = Q - W
Where:
ΔU = change in internal energy of the gas
Q = heat added to the gas
W = work done by the gas
In this case, the process is isothermal (constant temperature), meaning there is no change in internal energy (ΔU = 0). Therefore, the equation simplifies to:
0 = Q - W
Given that 150 kcal of heat (Q) was given off, we need to convert it to joules for consistency. Recall that 1 kcal is equal to 4.184 kJ (kilojoules).
150 kcal = 150 * 4.184 kJ = 627.6 kJ
Now we can solve for the work done (W):
0 = 627.6 kJ - W
Therefore, the work done by the gas is 627.6 kJ.