when 1240 J of heat are added to one mole of an ideal monatomic gas its temperature increases from 273K to 277K. Find the work done by the gas during the process.
To find the work done by the gas during the process, we can use the first law of thermodynamics.
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added (Q) minus the work done (W) on the system:
ΔU = Q - W
Since the gas is an ideal monatomic gas, the change in internal energy can be expressed as:
ΔU = (3/2)nRΔT
where n is the number of moles and R is the molar gas constant.
Given that one mole of the gas is heated from 273 K to 277 K, the change in temperature (ΔT) is 277 K - 273 K = 4 K.
We can substitute the values and rearrange the equation to solve for the work done:
ΔU = Q - W
(3/2)nRΔT = Q - W
W = Q - (3/2)nRΔT
We know the heat added (Q) is 1240 J and the number of moles (n) is 1. The molar gas constant (R) is 8.314 J/(mol·K).
Now we can substitute these values to find the work done:
W = 1240 J - (3/2)(1)(8.314 J/(mol·K))(4 K)
W = 1240 J - (6.228 J/K)(4 K)
W = 1240 J - 24.912 J
W = 1215.088 J
Therefore, the work done by the gas during the process is approximately 1215.088 J.
To find the work done by the gas during the process, we need to use the First Law of Thermodynamics, which relates the change in internal energy (ΔU) of a system to the heat transferred (Q) and the work done (W) during a process.
According to the First Law of Thermodynamics: ΔU = Q - W
Here, ΔU represents the change in internal energy, Q represents the heat transferred, and W represents the work done.
We are given that 1240 J of heat (Q) is added to the system. Therefore, Q = 1240 J.
We need to find the work done (W) by the gas. For an ideal gas, the internal energy change is related to the temperature change by the equation:
ΔU = (3/2) * n * R * ΔT
Where n represents the number of moles of the gas, R is the ideal gas constant, and ΔT is the change in temperature.
For a monatomic gas, the internal energy change is (3/2) * n * R * ΔT.
Given that the temperature increased from 273 K to 277 K, we can calculate the change in temperature as follows:
ΔT = Final temperature - Initial temperature
= 277 K - 273 K
= 4 K
Substituting the values into the equation for ΔU, we get:
ΔU = (3/2) * n * R * ΔT
ΔU = (3/2) * 1 * R * 4
ΔU = 6R
Now, let's substitute the known values and solve for W.
ΔU = Q - W
6R = 1240 J - W
To find the value of W, we need to know the value of the ideal gas constant (R), which is different depending on the units used. The commonly used value is 8.314 J/(mol·K).
Let's use this value of R and solve for W:
6 * 8.314 J/(mol·K) = 1240 J - W
49.884 J/mol = 1240 J - W
Now, we can isolate W:
W = 1240 J - 49.884 J/mol
W = 1190.116 J
Therefore, the work done by the gas during the process is approximately 1190.116 J.