Heat Q is added to a monatomic ideal gas at constant pressure. As a result, the gas does work W. Find the ratio Q/W.
What in the world is this asking??
Imagine in a balloon with perfectly stretchy walls
as you add Q, the gas expands keeping the pressure constant
That means that work is done pressure * area times expansion distance or integral of p dV. Meanwhile the gas heats up.
Look up constant pressure expansion.
W = n R delta T
Q = n Cp delta T
Q/W = n Cp delta T/n R delta T
= Cp/R
BUT for an ideal monatomic gas
Cp = 5R/2
so here
Q/W = 5/2
OMG. That was correct. Thank you. I'll never know how you people do this.
:)
You are welcome.
Most of us started a while ago.
This question is asking you to find the ratio of the heat added to a monatomic ideal gas at constant pressure to the work done by the gas.
To understand this question, it helps to have some background knowledge about the behavior of gases and the concepts of heat and work.
In the case of a monatomic ideal gas, it is assumed that the gas consists of individual particles (atoms) that behave like point masses with no internal structure. This type of gas obeys the ideal gas law and its behavior can be described by certain thermodynamic variables, such as pressure, volume, temperature, and the number of particles.
Heat (Q) refers to the transfer of energy that occurs due to a temperature difference. When heat is added to a gas, its temperature usually increases, and the thermal energy of the gas particles increases as well.
Work (W), on the other hand, refers to the energy transfer that occurs due to a force acting over a distance. In the case of a gas, work can be done when the gas expands or compresses, resulting in a change in volume. The gas can do work on its surroundings, or work can be done on the gas by an external force.
In this question, we are assuming that heat is added to the gas at constant pressure. This means that the pressure remains constant during the process, while the volume may change.
To find the ratio Q/W, you need to determine the amount of heat added (Q) and the work done (W). The ratio Q/W will then give you the relationship between the two.
To calculate Q, you need to know the specific heat capacity of the gas at constant pressure (Cp), which is a property of the gas. Cp represents the amount of heat required to raise the temperature of one mole of the gas by one degree at constant pressure. Therefore, Q can be calculated using the equation Q = n * Cp * ΔT, where n is the number of moles of the gas and ΔT is the change in temperature.
To calculate W, you need to know the change in volume (ΔV) during the process and the pressure (P) of the gas. The work done by the gas can be expressed as W = -P * ΔV, where -P indicates that work is done by the gas on its surroundings (positive work) when expansion occurs.
Once you have determined the values of Q and W, you can then calculate the ratio Q/W.