dE - q _ w
w = -340 J
dE = 8450 J
Solve for q.
q = mass gas x specific heat x (Tfinal-Tinitial)
Substitute and solve for specific heat.
What is the specific heat of the gas for this process?(J/(Kg.K))
w = -340 J
dE = 8450 J
Solve for q.
q = mass gas x specific heat x (Tfinal-Tinitial)
Substitute and solve for specific heat.
Mathematically, this can be expressed as:
ΔU = Q - W,
where ΔU is the change in internal energy, Q is the heat added, and W is the work done.
In this case, we are given that the internal energy increases by 8450 J and the work done by the gas is 340 J.
Substituting these values into the equation, we have:
8450 J = Q - 340 J.
To solve for Q, we rearrange the equation:
Q = 8450 J + 340 J.
Adding the values, we find:
Q = 8790 J.
Therefore, the heat transferred to the gas is 8790 J.
To find the specific heat of the gas, we use the formula:
Q = mcΔT,
where Q is the heat transferred, m is the mass of the gas, c is the specific heat, and ΔT is the change in temperature.
Rearranging the equation to solve for c, we have:
c = Q / (m * ΔT).
We are given that the mass of the gas is 0.0800 kg, and the temperature change is from 25°C to 225°C.
Substituting these values into the equation, we have:
c = 8790 J / (0.0800 kg * (225°C - 25°C)).
Calculating the denominator first:
c = 8790 J / (0.0800 kg * 200°C).
Finally, evaluating the expression:
c = 8790 J / 16.0 kg°C.
Hence, the specific heat of the gas for this process is approximately 549.38 J/(kg·K).
ΔU = Q + W
Where:
ΔU is the change in internal energy of the gas,
Q is the heat transferred to the gas,
and W is the work done by the gas.
From the given information:
ΔU = 8450 J
W = 340 J
Substituting these values into the equation, we have:
8450 J = Q + 340 J
To find the value of Q, we can rearrange the equation as:
Q = 8450 J - 340 J
Q = 8110 J
Therefore, the amount of heat transferred to the gas is 8110 J.
Now, to find the specific heat of the gas for this process (c), we can use the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred to the gas (8110 J),
m is the mass of the gas (0.0800 kg),
c is the specific heat of the gas,
and ΔT is the change in temperature (225°C - 25°C = 200°C).
Substituting these values into the equation, we have:
8110 J = 0.0800 kg * c * 200°C
To isolate c, we can rearrange the equation as:
c = 8110 J / (0.0800 kg * 200°C)
c = 50.69 J/(kg·K)
Therefore, the specific heat of the gas for this process is 50.69 J/(kg·K).