- #1
dk_ch
- 44
- 0
Homework Statement
An ideal gas(γ=1.4) was expanded under constant pressure. The work done was 80 Joule.Calculate the heat absorbed and increase in internal energy of the system.
Feodalherren said:Well, what's the equation for a gas undergoing expansion under constant pressure?
[itex]w= P \int dV[/itex]
Feodalherren said:I'm not just going to give you the solution. You won't learn anything. You need to show some work and initiative and I can guide you through it.
Start by thinking about this: is the change in energy path dependent or path independent?
Feodalherren said:And I actually get stuck there too.. Hmm. You aren't given either moles of gas or change in temperature? With your gamma you can find Cp and Cv but you don't seem to have enough information.
[itex]Q = nC_{p} \Delta T[/itex]
and [itex]\Delta E = nC_{v} \Delta T[/itex]
Ah! Genius. I would never have thought of that :).CAF123 said:Divide these two equations and you will get Q/ΔE = cp/cv = γ = 1.4. Along with the equation from conservation of energy, you now have two equations with two unknowns.
CAF123 said:Divide these two equations and you will get Q/ΔE = cp/cv = γ = 1.4. Along with the equation from conservation of energy, you now have two equations with two unknowns.
The formula for calculating heat absorbed is Q = mcΔT, where Q is the heat absorbed, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.
Specific heat capacity is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius.
Sure, for example, if we have a 500-gram block of iron with a specific heat capacity of 0.45 J/g°C and it's heated from 20°C to 50°C, the heat absorbed would be Q = (500 g)(0.45 J/g°C)(50°C - 20°C) = 9,000 J.
The units for heat absorbed are Joules (J) in the metric system and calories (cal) in the imperial system.
Heat absorbed is the amount of heat energy that is gained by an object, while heat released is the amount of heat energy that is lost by an object. They are both measured in the same units (Joules or calories) but have opposite effects on the temperature of the object.