Solving Thermodynamics Problems: Compute C_v and Heat Capacity

[cukitas2001]

ok these last few problems have been driving me up a wall an of course its got to be something simple I am missing.

1)
A) Compute the specific heat capacity at constant volume of nitrogen ($$N_2$$) gas. The molar mass of $$N_2$$ is 28.0grams/mol.

the heat capacity of a diatomic molecule is:
$$C_v =\frac{5}{2} R$$ but i don't think this is what I am suppsoed to use? help please

B) You warm 1.10kg of water at a constant volume from 18.0 celsius to 30.5 celsius in a kettle. For the same amount of heat, how many kilograms of 18.0 celsius air would you be able to warm to 30.5 degrees? Make the simplifying assumption that air is 100% $$N_2$$.

C)What volume would this air occupy at 18.0 celsisu and a pressure of 1.11 atm ?

I'm pretty sure if i figure out B i can solve C

2)
A) How much heat does it take to increase the temperature of n moles of a diatomic ideal gas by an amount $$\Delta\,T$$near room temperature if the gas is held at constant volume? Use R for ideal gas constant.

Well $$C_v =\frac{5}{2} R$$ but this doesn't include any temperature changes so what else is available to use?

B)What is the answer to the question in part (A) if the gas is monatomic rather than diatomic?

Again i think if i can figure out A i can answer B

3) this is posted in another thread so check out my other thread please

nvm figured these out but still need help on the question in other thread...help pleasse

 

[lightgrav]

1a) Why not use it ... isn't N_2 diatomic?
The issue is to get Specific Heat Capacity in familiar units ... [J/kg/K].
1b) The ambiguity here is that Cv (part a) is NOT equal to Cp.
1c) Apparently, this air is in a Pressure container, so it CAN be kept at V.

2) "doesn't include any Temperature change" What do you think Cv IS?

 

[kyle8921]

I can understand your frustration with these problems. Thermodynamics can be a complex topic, and it's common to overlook simple solutions when we get stuck on a problem. Let's break down each of these problems and see if we can find a solution together.

1) A) To compute the specific heat capacity at constant volume of nitrogen gas, we can use the equation C_v = (5/2)R, where R is the universal gas constant. However, we need to convert the given molar mass of N_2 into kilograms, so we can use R = 8.314 J/mol*K. This gives us a value of C_v = 20.79 J/mol*K.

B) To solve this problem, we can use the equation Q = mC_vΔT, where Q is the heat transferred, m is the mass of the substance, C_v is the specific heat capacity at constant volume, and ΔT is the change in temperature. We can rearrange this equation to solve for m, giving us m = Q/(C_vΔT). Plugging in the given values, we get m = (1.10 kg)(4186 J/kg*K)(12.5 K)/(20.79 J/mol*K)(11.5 K) = 2.05 kg of air.

C) To find the volume of this air at 18.0 celsius and 1.11 atm, we can use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Rearranging this equation, we get V = nRT/P. We know the number of moles of air is equal to the number of moles of N_2 in 2.05 kg, which is (2.05 kg)(1000 g/kg)/(28.0 g/mol) = 73.2 mol. Plugging in the values, we get V = (73.2 mol)(8.314 J/mol*K)(291.15 K)/(1.11 atm) = 17,519 L.

2) A) To find the heat required to increase the temperature of n moles of a diatomic ideal gas by ΔT, we can use the equation Q = nC_vΔT. Plugging in the given values, we get