An 80.0-gram sample of a gas was heated from 25 °C to 225 °C. During this process, 346 J of work was done by the system and its internal energy increased by 6365 J. What is the specific heat of the gas?
To find the specific heat of the gas, we need to use the formula:
ΔU = Q - W
where ΔU is the change in internal energy of the system, Q is the heat added to the system, and W is the work done by the system.
Given that the internal energy increased by 6365 J and the work done by the system is 346 J, we can substitute these values into the equation:
6365 J = Q - 346 J
Now, we can solve for Q by rearranging the equation:
Q = 6365 J + 346 J
Q = 6711 J
The heat added to the system, Q, is the same as the heat gained or lost by the gas. Since the specific heat (c) is defined as the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius, we can calculate the specific heat by dividing the heat gained by the mass of the gas and the change in temperature:
c = Q / (m * ΔT)
where c is the specific heat, m is the mass of the gas, and ΔT is the change in temperature.
Given that the mass of the gas is 80.0 grams and the change in temperature is 225 °C - 25 °C = 200 °C, we can substitute these values into the equation:
c = 6711 J / (80.0 g * 200 °C)
c ≈ 0.419 J/(g·°C)
Therefore, the specific heat of the gas is approximately 0.419 J/(g·°C).
dE = q + w
w = -346J from the problem.
dE increased by 6365 J.
Solve for q
Then q = mass x specific heat x (Tfinal-Tinitial)
Substitute and solve for sp. h.