7.Question 7A rigid container holds an ideal gas with c_v = 0.75 kJ/(kgK). The container is cooled from 110 ℃ to 20 ℃. Find the specific heat transfer (kJ/kg) for the process. 1 point-96 kJ/kg96 kJ/kg67.5 kJ/kg-67.5 kJ/kg
Question
7.Question 7A rigid container holds an ideal gas with c_v = 0.75 kJ/(kgK). The container is cooled from 110 ℃ to 20 ℃. Find the specific heat transfer (kJ/kg) for the process. 1 point-96 kJ/kg96 kJ/kg67.5 kJ/kg-67.5 kJ/kg
Solution
The specific heat transfer can be calculated using the formula:
q = m * c_v * (T_final - T_initial)
where:
- q is the heat transfer,
- m is the mass of the gas,
- c_v is the specific heat capacity at constant volume,
- T_final is the final temperature, and
- T_initial is the initial temperature.
However, in this case, we are looking for the specific heat transfer (per unit mass), so we can ignore the mass in the calculation. Also, the temperatures need to be in Kelvin for the calculation.
First, convert the temperatures from Celsius to Kelvin. The conversion is done by adding 273.15 to the Celsius temperature:
T_initial = 110°C + 273.15 = 383.15 K T_final = 20°C + 273.15 = 293.15 K
Then, substitute the values into the formula:
q = c_v * (T_final - T_initial) q = 0.75 kJ/(kgK) * (293.15 K - 383.15 K) q = -67.5 kJ/kg
So, the specific heat transfer for the process is -67.5 kJ/kg. The negative sign indicates that heat is being removed from the system (since the gas is being cooled).
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