What is the approximate energy required to raise the temperature of 5 L of air by 160 °C? The volume is held constant. (Assume air almost entirely consists of nitrogen, oxygen, and argon, and that it is initially at 273 K. Use the numerical data found in this table on the composition of the atmosphere and found in this table containing molar specific heat values.)
To calculate the energy required to raise the temperature of a substance, you can use the formula:
Q = m * C * ΔT
Where:
- Q is the energy in Joules (J)
- m is the mass of the substance in kilograms (kg)
- C is the specific heat capacity of the substance in J/kg·°C
- ΔT is the change in temperature in °C
In this case, we will need to calculate the mass of the air using the given volume and the density of air. Then, we can find the specific heat capacity of air using the molar specific heat values provided. Let's break it down step by step:
Step 1: Calculate the mass of 5 L of air
To find the mass of air, we need to know its density. The composition of air is given, so we can use the molar masses of nitrogen (N₂), oxygen (O₂), and argon (Ar) to calculate the density using the ideal gas law.
The molar masses of the gases are as follows:
- Nitrogen (N₂): 28.0134 g/mol
- Oxygen (O₂): 31.9988 g/mol
- Argon (Ar): 39.948 g/mol
Using the composition of air (approximately 78% nitrogen, 21% oxygen, and 1% argon) and the molar masses, we can calculate the average molar mass of air (M_air).
M_air = (0.78 * M_N₂) + (0.21 * M_O₂) + (0.01 * M_Ar)
Step 2: Calculate the mass of 5 L of air
Now that we have the average molar mass of air, we can calculate the mass using the ideal gas law:
PV = nRT
Where:
- P is the pressure (assume constant and cancel it out)
- V is the volume of air (5 L)
- n is the number of moles of air (which is the given air volume divided by the molar volume)
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the initial temperature (273 K)
n = V / V_molar (where V_molar is the molar volume)
Step 3: Calculate the specific heat capacity of air
The specific heat capacity is given as molar specific heat values for each gas. We can calculate the average specific heat capacity of air (C_air) using the composition and the molar specific heat values. Each molar specific heat value needs to be multiplied by the molar fraction of that gas in air.
C_air = (0.78 * C_N₂) + (0.21 * C_O₂) + (0.01 * C_Ar)
Step 4: Calculate the energy
Using the mass of air and the specific heat capacity, we can now calculate the energy required:
Q = m * C_air * ΔT
Substitute the values into the equation and calculate Q.
Please note that the specific heat values and molar masses used may vary slightly depending on the specific sources, so be sure to refer to the provided tables for accurate data.