# What kind of damage would a thunder punch do?

The character I'm working om has the ability to compress/decompress air in a 2 foot radius around his body. His signature move is the "Thunder Punch" in which he compresses the air in front of his fist and creates a shockwave upon impact with the target.

How much damage would the shockwave a thunderclap produces deal to a human point blank?

Edit: I'm not asking about the effects or survivability of the shockwave. I'm asking precisely how much damage the shockwave produced from a 2 foot radius sphere of compressed air being released would do.

• Possible duplicate of Sonic Boom Effects on Human Anatomy. – Frostfyre Apr 20 '17 at 12:35
• @MolbOrg Reading your comments I feel you and I have different views of what constitutes story based. Could you run me through your criteria? – Bellerophon Apr 20 '17 at 13:38
• @kingledion yes, probably paid not enough attention to the information provided in the question. I retract the vote. – MolbOrg Apr 20 '17 at 13:39
• @Bellerophon I'm working on the set of the rules at the moment, but firstly I have to pay more attention to the questions, as in the case. Feel free to point me in the cases you are interested, I will try to clarify and it will help me to work out the rules faster, sometimes I make mistakes. – MolbOrg Apr 20 '17 at 13:43
• btw, the answer to the question "I'm asking precisely how much damage the shockwave produced from a 2 foot radius sphere of compressed air being released would do." - practically any amount of damage, as it is not specified how much he can compress the volume, why he can't use a continuous stream of air which will flow in the 2ft sphere in the time he compresses the first portion, I begin to fear that the earth integrity is no safe in the case. – MolbOrg Apr 20 '17 at 14:14

# Depends on the process

This is a tricky one to answer, because it depends on what thermodynamic processes you are talking about.

For example, if his power allows him to compress the gas into a tiny ball, and then release it to go bang, there will not be any work (or bang) done. This is called adiabatic free expansion of a gas.

# Lets make it isothermal

In order to do work and make a bang the way you are wanting, the process must be made isothermal. This is a reversible, constant temperature change. In order to keep temperature constant, your protagonist's power must include absorbing energy from the compressed gas to keep its temperature constant, then releasing that energy with the expansion.

In that case, the work done is $$W_{1\rightarrow 2} = -nRT\log{\frac{V_2}{V_1}}.$$

A 2 foot radius sphere is 0.6096 meters radius in science units, and 0.949 m$^3$ in volume. A mol of ideal gas at standard pressure and temperature occupies 22.4 liters, so there are 42.3 mols of air in the compressed air. Standard temperature is 273 K. The ideal gas constant is 8.314 J / K / mol.

We can now do the calculation if we make some assumptions about how tightly the gas can be compressed. As you can see, the final compressed volume is a variable, and we can set it as we like. Either way you will get a lot of energy out thi way.

If we assume the gas is compressed into a 1 cm radius dot, we get a final volume of 4.19e-3 m$^3$, and energy of $$-nRT\log\frac{V_2}{V_1} = 42.3 \text{mol} \cdot 8.314 \frac{\text{J}}{\text{K}\cdot\text{mol}}\cdot 273 \text{K} \log\frac{0.949 \text{ m}^3}{4.19\times10^{-6} \text{ m}^3} = 1.2 \text{MJ}$$

1.2 MJ is almost 100 times the energy of a .50 cal round. That's a lot of juice! Your only problem now is keeping your protagonist from being killed by his own blast.

• So, because gases heat up when compressed, he'd need to absorb the heat produced and then release the compressed air and heat simultaneously to do work in the system? All due to free expansion. – AJ D. Apr 20 '17 at 1:00
• Precisely. But if you do it this way you get a LOT of energy. – kingledion Apr 20 '17 at 1:10
• Your only problem now is keeping your protagonist from being killed by his own blast Easy. Required Secondary Powers – Draco18s Apr 20 '17 at 3:58
• Isothermally related: "Startup says it can make compressed-air energy storage scheme dirt cheap" by Megan Geuss on Ars Technica. – AlexP Apr 20 '17 at 13:23