how to solve this problem 3. Five moles of an ideal monatomic gas with an initial temperature of 127 °C expand and, in the process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas?
pls.. help me with this i really need it.. pls.
A gas in a cylinder expands from a volume of 0.110 m3 to 0.320 m3. Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 x 105 Pa during the expansion. The total heat added is 1.15 x 105 J. (a) Find the work done by the gas. (b) Find the change in internal energy of the gas. (c) Does it matter whether the gas is ideal? Why or why not?
To solve this problem, we need to 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, it can be represented as:
ΔU = Q - W
Where:
ΔU is the change in internal energy
Q is the heat added to the system
W is the work done by the system
In this case, we have the following information:
Initial temperature (Ti) = 127 °C
Heat added (Q) = 1200 J
Work done (W) = 2100 J
Number of moles (n) = 5
First, we need to calculate the change in internal energy (ΔU) using the first law of thermodynamics:
ΔU = Q - W
ΔU = 1200 J - 2100 J
ΔU = -900 J
Since we have an ideal monatomic gas, the change in internal energy can be related to the change in temperature (ΔT) using the following equation:
ΔU = (3/2)nRΔT
Where:
n is the number of moles (in this case, 5)
R is the gas constant (8.314 J/(mol·K))
Substituting the given values and rearranging the equation, we can solve for ΔT:
-900 J = (3/2)(5)(8.314 J/(mol·K))(ΔT)
-900 J = 37.71 J/(mol·K) · (ΔT)
Dividing both sides of the equation by 37.71 J/(mol·K), we have:
(ΔT) = -900 J / (37.71 J/(mol·K))
(ΔT) = -23.858 K
The negative sign indicates that the final temperature is lower than the initial temperature. To find the final temperature (Tf), we need to subtract the change in temperature from the initial temperature:
Tf = Ti + ΔT
Tf = 127 °C - 23.858 K
Tf = 103.142 °C
Therefore, the final temperature of the gas is approximately 103.142 °C.