How Long to Heat Ammonia Gas by 12°C with Solar Power?

[cash.money]

Homework Statement

The sun heats 2.00 x 10^2 kg of ammonia gas that is kept at constant volume in a large tank. Assuming that solar radiation of 6.00 x 10^2 W caused the heating, determine the length of time it took to raise the ammonia's temperature by 12°C.

Homework Equations

The Attempt at a Solution

 

[Andrew Mason]

Homework Statement

The sun heats 2.00 x 10^2 kg of ammonia gas that is kept at constant volume in a large tank. Assuming that solar radiation of 6.00 x 10^2 W caused the heating, determine the length of time it took to raise the ammonia's temperature by 12°C.

You will have to show us what you have done. How many moles of ammonia do you have? What is the molar heat capacity of ammonia gas at constant volume?

AM

 

[nlightner]

To solve this problem, we can use the formula Q = mcΔT, where Q is the heat absorbed, m is the mass of the gas, c is the specific heat capacity, and ΔT is the change in temperature. First, we need to calculate the heat absorbed by the ammonia gas. We know that the solar radiation is the source of heat, so we can use the formula P = Q/t, where P is the power of the radiation, Q is the heat absorbed, and t is the time. Plugging in the given values, we get Q = (6.00 x 10^2 W)(t).

Next, we need to calculate the specific heat capacity of ammonia gas. According to the International Union of Pure and Applied Chemistry, the specific heat capacity of ammonia gas is 2.08 J/g·K. Converting the mass of the gas from kg to g, we get 2.00 x 10^5 g.

Now, we can plug in all the values into the formula Q = mcΔT. We know that the temperature change is 12°C, so ΔT = 12 K. Plugging in the values, we get (6.00 x 10^2 W)(t) = (2.00 x 10^5 g)(2.08 J/g·K)(12 K).

Solving for t, we get t = 5 x 10^2 seconds, or 8.33 minutes. Therefore, it took approximately 8.33 minutes for the sun to raise the temperature of the ammonia gas by 12°C.