1.0 mol of argon has 3100 J of thermal energy. What is the gas temperature in °C?

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Hi, everyone. In this breakfast problem, we will have a container holding 1.5 moles of neon gas possessing 2500 joles of thermal energy. We are being asked to calculate the temperature of the gas in degrees Celsius. And the options given are a negative 100 and 40 degrees Celsius B negative 100 and 26 degrees Celsius, C negative 100 and 10 degrees Celsius and D negative and 46 degrees Celsius. So to find the temperature of the neon gas, we can use the formula for the internal energy of a mo atomic ideal gas. So U will be the um internal energy D U will then be equals to three divided by two, multiplied by N RT U is the internal energy as I have described previously and is the number of moles, R is the gas constant and D is the temperature in Calvin. In the problem statement, it is given that our U is 2500 Joles and our N is 1.5 mole. We note that the gas constant or R is 8.314 Joles divided by mole Kelvin. So um the only thing that is left here is just calculating the temperature. So we can rearrange the U equation here to get an equation for our temperature where the temperature will then be equals to two divided by three multiplied by U divided by an R. So this is the final equation that we are going to be using. So then our T can then be calculated by substituting all of our values into our equation where T will then be equals to two divided by three, multiplied by U which is 2500 jules divided by N which is 1.5 mole and then multiply it by R which is 8.314 jules divided by mole Calvin calculating this, we will get our temperature to then be equals to 100 and 33.64 Kelvin. However, what's being asked is the temperature of the gas in degrees Celsius. So we have to convert this into degrees Celsius. So our temperature is 100 and 33. Kelvin and converting that into degrees Celsius. We just have to minus this with 273.15 Kelvin. Um doing this calculation, we will then get our temperature in Celsius which will then be negative 100 and 40 degrees Celsius. So the temperature of the neon gas is approximately negative 100 and degrees Celsius which will correspond to option A in our answer. Choices. So option A will be the answer to this particular practice problem and that'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our other lesson videos on similar topics available on our website and that will be it for this one. Thank you.

1.0 mol of argon has 3100 J of thermal energy. What is the gas temperature in °C?

Verified Solution

Key Concepts

Thermal Energy

Ideal Gas Law

Temperature Conversion