Heat added to Monatomic Gas at Constant Pressure

[KendrickLamar]

Homework Statement

If 650 J of heat are added to 21 moles of a monatomic gas at constant pressure, how much does the temperature of the gas increase? (in Kelvins)

Homework Equations

U = nRT
Q=(5/2)nR(T2-T1)

The Attempt at a Solution

well how do you even know how much the temperature changes by if they don't give u an initial temperature? or is it just as simple as solving for delta T in which you just do

650J = (5/2)(21)( 8.31 J/mol.K )(Delta T)

is it really that simple or do i have to do something with the 21 moles and convert it or anything? and once i do get the Delta T must that be converted or something in order to have it end up in Kelvins? I ended up with 1.4899K I am not sure if that's right though.

 

[ehild]

It is correct. Do not write it out with more than 3 digits. ehild

 

[Andrew Mason]

Homework Statement

If 650 J of heat are added to 21 moles of a monatomic gas at constant pressure, how much does the temperature of the gas increase? (in Kelvins)

Homework Equations

U = nRT

Careful. For a monatomic ideal gas, internal energy, U = 3nRT/2

Q=(5/2)nR(T2-T1)

Note that T is in Kelvins, and Q is in Joules and R is in Joule/mol Kelvin. The molar heat capacity Cp (=5R/2) is temperature independent ie. it is the same for all T.

The Attempt at a Solution

well how do you even know how much the temperature changes by if they don't give u an initial temperature? or is it just as simple as solving for delta T in which you just do

650J = (5/2)(21)( 8.31 J/mol.K )(Delta T)

is it really that simple ...

It is that simple.

AM

 

[KendrickLamar]

wait so is it 3/2 or 5/2? because i have 2 equations from the formula sheet he gave us one says

Cp = 5/2 * R and one says Cv = 3/2 * R ? or in this case is it the 3/2*5/2 or something?

 

[ehild]

Cp is the molar specific heat capacity at constant pressure, and it is 5/2 R for mono-atomic gases. You add heat at constant pressure, so Cp was correctly used.

ehild

 

[KendrickLamar]

thank you guys, appreciate it a lot

 

[Andrew Mason]

wait so is it 3/2 or 5/2? because i have 2 equations from the formula sheet he gave us one says

Cp = 5/2 * R and one says Cv = 3/2 * R ? or in this case is it the 3/2*5/2 or something?

Cp = 5R/2 and Cv=3R/2. But you had U = nRT. That is not correct. U = nCvT = (3/2)nRT.

AM