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 8905 J. What is the specific heat of the gas?
Specific Heat= (quantity of heat trandferred in Joules) / (mass of substance in grams) * (temperature change)
To find the specific heat of the gas, we need to use the equation:
Q = mcΔT
Where:
Q is the heat transferred to the system
m is the mass of the gas
c is the specific heat capacity of the gas
ΔT is the change in temperature
In this case, we are given:
m = 80.0 g
ΔT = 225 °C - 25 °C = 200 °C
Q = 8905 J
First, we need to calculate the heat transferred (Q) from the internal energy change and the work done:
ΔU = Q + W
Where ΔU is the change in internal energy, Q is the heat transferred, and W is the work done.
Given that ΔU = 8905 J and W = 346 J, we can rearrange the equation to solve for Q:
Q = ΔU - W
Q = 8905 J - 346 J
Q = 8559 J
Now, we can plug in the values we have into the specific heat equation:
8559 J = (80.0 g) * c * (200 °C)
To solve for c, divide both sides of the equation by (80.0 g) * (200 °C):
c = 8559 J / (80.0 g * 200 °C)
c ≈ 0.536 J/g·°C
So, the specific heat of the gas is approximately 0.536 J/g·°C.