An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8,000 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant.
(a) How much work is done on the gas as the temperature of 0.230 mol of the gas is raised from 25.0°C to 290°C?
J
(b) What does the sign of your answer to part (a) indicate?
The surroundings do positive work on the gas. There is no work done, by the gas or the surroundings. The gas does positive work on its surroundings
To calculate the work done on the gas, we can use the equation:
W = PΔV
Where:
W is the work done on the gas,
P is the pressure exerted by the gas, and
ΔV is the change in volume of the gas.
Since the pressure of the gas remains constant, we can rewrite the equation as:
W = P(V2 - V1)
Where:
V1 is the initial volume of the gas, and
V2 is the final volume of the gas.
To find V1 and V2, we need to use the ideal gas law:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature of the gas.
Rearranging the ideal gas law equation, we get:
V = (nRT) / P
Given:
n = 0.230 mol
R = 8.314 J/(mol·K)
T1 = 25.0°C = 25.0 + 273.15 K
T2 = 290°C = 290 + 273.15 K
Now we can calculate V1 and V2:
V1 = (nRT1) / P
V2 = (nRT2) / P
Once we have V1 and V2, we can find the difference in volume and plug it back into the work equation to calculate the work done on the gas.
Let's proceed with the calculations:
First, convert the temperature to Kelvin:
T1 = 25.0 + 273.15 = 298.15 K
T2 = 290 + 273.15 = 563.15 K
Next, calculate V1:
V1 = (0.230 mol * 8.314 J/(mol·K) * 298.15 K) / P
Given that the pressure of the gas remains constant, we can assume that the pressure exerted by the gas is the same as the pressure on the piston. But the problem does not provide the pressure value. Therefore, we cannot calculate the exact work done on the gas without knowing the pressure.
Finally, calculate V2:
V2 = (0.230 mol * 8.314 J/(mol·K) * 563.15 K) / P
Again, without knowing the pressure, we cannot calculate the exact work done on the gas.
So, it is not possible to determine the value of work done on the gas (part a) or the sign of the work done (part b) without knowing the pressure of the gas.