How to find added thermal heat in monoatomic gas?

[Helly123]

Homework Statement

for number 3,4,5 I'm still trying

Homework Equations

PV/T = PV/T
q = ΔU + W
W = P ΔV

The Attempt at a Solution

(3) I used PV/T = PV/T to find the ΔT for each process
for A→B I find PV/TA = P3V/TB ----- TB = 3TA (T increase)
for B→C I find P3V/TB = 4P3V/TC ----- TC = 4TB (T increase)
for C→D I find 4P3V/TC = 4PV/TD ----- TD = ⅓TC (T decrease)
for D→A I find 4PV/TD = PV/TA ----- TA = ¼TD (T decrease)

so I drew a conclusion that among 4 process , gas received from outside max at process B→C
are the answer and the reason right?

(4) at process B→C there's no ΔV. So, W = 0
q = ΔU + 0
q = the amount of heat added or removed from system
So, the question for (4) Is to find q at process B→C ?
q for monoatomic gas is 3/2nKT
but what's the n (mol) known?
can you give me some clue to answer (4)?

(5) now the heat that gas emits,
I thought there are 2 W :
W at A→B = P.(3V - V) = 2PV
W at C→D = 4P(V-3V) = -8PV (minus ?)
can you give me some clue to answer (5)?

 

[I like Serena]

Hi Helly,

Let's bring in a couple more equations.
For an ideal gas we have PV=nRT.
And for a monatomic ideal gas we have U=3/2 nRT, where R is the molar gas constant (R=8.31 J/K.mol).

(3) I used PV/T = PV/T to find the ΔT for each process
for A→B I find PV/TA = P3V/TB ----- TB = 3TA (T increase)
for B→C I find P3V/TB = 4P3V/TC ----- TC = 4TB (T increase)
for C→D I find 4P3V/TC = 4PV/TD ----- TD = ⅓TC (T decrease)
for D→A I find 4PV/TD = PV/TA ----- TA = ¼TD (T decrease)

so I drew a conclusion that among 4 process , gas received from outside max at process B→C
are the answer and the reason right?

The question asks about the thermal heat, which is q, and not the change in temperature.
Can we calculate q for each of the processes?

(4) at process B→C there's no ΔV. So, W = 0
q = ΔU + 0
q = the amount of heat added or removed from system
So, the question for (4) Is to find q at process B→C ?
q for monoatomic gas is 3/2nKT
but what's the n (mol) known?
can you give me some clue to answer (4)?

The number of moles is given to be 1 mol.
And we can use that PV=nRT for an ideal gas (I'm assuming that your K is the same as R).

(5) now the heat that gas emits,
I thought there are 2 W :
W at A→B = P.(3V - V) = 2PV
W at C→D = 4P(V-3V) = -8PV (minus ?)
can you give me some clue to answer (5)?

The net heat is equal to the area inside the graph, which is also equal to the total work done during the process.
Can we find those?

 

[Helly123]

Hi Helly,

Let's bring in a couple more equations.
For an ideal gas we have PV=nRT.
And for a monatomic ideal gas we have U=3/2 RT, where R is the molar gas constant (R=8.31 J/K.mol).
The question asks about the thermal heat, which is q, and not the change in temperature.
Can we calculate q for each of the processes?
The number of moles is given to be 1 mol.
And we can use that PV=nRT for an ideal gas (I'm assuming that your K is the same as R).
The net heat is equal to the area inside the graph, which is also equal to the total work done during the process.
Can we find those?

Thanks Serena for all the clues and explanation, I'll try it :)