Temperature Change in Adiabatic Process for Ideal Monatomic and Diatomic Gases

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In an adiabatic process, the temperature change of an ideal monatomic gas can be calculated using the work done on the gas, which is 2.0 kJ per mole. For monatomic gases, the temperature change is derived from the relationship between internal energy and work, where dU = -W. For diatomic gases, the calculation also considers molecular rotation, affecting the temperature change differently than for monatomic gases. The relevant equations include the adiabatic condition pV^y = constant and TV^(y-1) = constant, which are essential for understanding the process. The discussion clarifies that this problem pertains to an introductory physics course focused on thermodynamic processes.
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Homework Statement


a) By how much does the temperature of an ideal monatomic gas change in an adiabatic process in which 2.0 kJ of work are done on each mole of gas?
b) By how much does the temperature of an ideal diatomic gas (with molecular rotation but no vibration) change in an adiabatic process in which 2.0 kJ of work are done on each mole of gas?

Homework Equations


Q = 0
dU = -W
W = (p_1 V_1 - p_2 V_2) / (y - 1)
pV^y = const.
TV^(y-1) = const.

The Attempt at a Solution


None, I have no idea how to approach this problem. Please help.
 
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Why is pV^y = const and TV^(y-1) = const relevant? Is this a polytropic process?
 
Also. What class is this for? Is it a physics course or a thermodynamics course? There are different approaches.
 
This is for an introductory physics course, and the book defines four different types of processes: Isothermal, Isometric, Isobaric, and Adiabatic (no heat transfer). I think I am supposed to use one of those, and it would be adiabatic since the problem mentions it.
 
I have managed to solve this problem. Thank you.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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