Part 1: Calculate the heat that must be supplied to
10.7 g of Ne(g) at 0.15 atm to raise its temperature
from 20◦C to 49◦C at constant pressure.
Assume that neon behaves as an ideal gas.
Answer in units of J.
Part 2: Calculate the heat at a constant volume. Answer in units of J.
I just don't get how to do it at all
Everything you need tied in a nice bow.
http://physics.bu.edu/~redner/211-sp06/class24/class24_heatcap.html
To calculate the heat (q) required for a process, you can use the formula:
q = n C ΔT
where:
- q is the heat
- n is the number of moles
- C is the molar heat capacity (Cp or Cv, depending on whether the process is at constant pressure or constant volume, respectively)
- ΔT is the change in temperature
Let's calculate the answers step-by-step:
Part 1: Calculate the heat at constant pressure
1. Convert the mass of Ne(g) to moles:
- The molar mass of Ne is approximately 20.18 g/mol.
- Divide the given mass (10.7 g) by the molar mass:
moles = 10.7 g / 20.18 g/mol
2. Determine the molar heat capacity at constant pressure (Cp) of Ne(g)
- The molar heat capacity for an ideal gas at constant pressure is generally given as 3/2R, where R is the ideal gas constant (8.314 J/(mol·K)).
- Cp = (3/2)R
3. Calculate the change in temperature (ΔT)
- ΔT = T2 - T1
- T2 = 49◦C + 273.15◦C (convert to Kelvin)
- T1 = 20◦C + 273.15◦C (convert to Kelvin)
4. Substitute the values into the formula and solve:
q = (moles) * (Cp) * (ΔT)
Part 2: Calculate the heat at constant volume
1. Determine the molar heat capacity at constant volume (Cv) of Ne(g)
- For an ideal monoatomic gas, the molar heat capacity at constant volume is given as (3/2)R.
2. Substitute the values into the formula and solve:
q = (moles) * (Cv) * (ΔT)
Let me know if you would like a detailed step-by-step calculation for these problems.
Part 1 explanation:
To calculate the heat that must be supplied to raise the temperature of a sample of gas at constant pressure, we can use the equation:
q = n × Cp × ∆T
Where:
q is the heat transferred to the gas (in joules, J),
n is the number of moles of the gas,
Cp is the molar heat capacity at constant pressure (in J/mol·K),
∆T is the change in temperature (in Kelvin).
Step 1: Determine the number of moles of Ne(g):
To find the number of moles, we use the equation:
n = mass / molar mass
Given that the mass of Ne(g) is 10.7 g, we need to know the molar mass of neon. The molar mass of neon is the sum of the atomic masses of the individual atoms in one mole of neon. The atomic mass of neon (Ne) is approximately 20.18 g/mol.
Using the equation:
n = 10.7 g / 20.18 g/mol
n ≈ 0.530 mol
Step 2: Calculate the change in temperature (∆T):
The change in temperature is calculated by subtracting the initial temperature from the final temperature. However, we need to convert the temperature from Celsius to Kelvin since temperature is always measured in Kelvin in thermodynamic calculations.
∆T = (Tfinal - Tinitial) + 273.15
Given Tinitial = 20°C = 293.15 K, and Tfinal = 49°C = 322.15 K:
∆T = (322.15 K - 293.15 K) = 29 K
Step 3: Determine the molar heat capacity at constant pressure (Cp):
For neon gas as an ideal gas at constant pressure, the molar heat capacity (Cp) is approximately 20.8 J/mol·K.
Step 4: Calculate the heat transferred (q):
Using the provided equation:
q = n × Cp × ∆T
q = (0.530 mol) × (20.8 J/mol·K) × (29 K)
q ≈ 315.53 J
Therefore, the heat that must be supplied to 10.7 g of Ne(g) to raise its temperature from 20°C to 49°C at constant pressure is approximately 315.53 J.
Part 2 explanation:
To calculate the heat at constant volume, we need to use the molar heat capacity at constant volume (Cv) instead of the molar heat capacity at constant pressure (Cp). The equation for calculating the heat at constant volume is similar, but we use Cv instead of Cp.
The molar heat capacity at constant volume (Cv) for neon gas is approximately 12.5 J/mol·K.
Using the same values as in Part 1, except substituting Cp with Cv in the equation:
q = n × Cv × ∆T
q = (0.530 mol) × (12.5 J/mol·K) × (29 K)
q ≈ 183.62 J
Therefore, the heat at constant volume for 10.7 g of Ne(g) to raise its temperature from 20°C to 49°C is approximately 183.62 J.