Question

При нагревании газа в закрытом сосуде на 80 К его давление увеличилось на 20%. Определить начальную температуру газа.

Answer 1

Ответ:

400 K

Объяснение:

ΔT=80 K     p2=1.2*p1      T1=?

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V=const

p1/T1=p2/T2

p1/T1=1.2*p1/(T1+ΔT)

T1=ΔT/0.2=80/0.2=400 K

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Answer 2

Problem Analysis

We are given that the pressure of a gas in a closed vessel increases by 20% when the gas is heated to 80 K. We need to determine the initial temperature of the gas.

Solution

Let's assume the initial temperature of the gas is T. According to the problem, when the gas is heated to 80 K, its pressure increases by 20%.

To solve this problem, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature (in Kelvin), assuming constant volume and amount of gas. Mathematically, it can be represented as:

P1/T1 = P2/T2

Where: - P1 is the initial pressure of the gas - T1 is the initial temperature of the gas - P2 is the final pressure of the gas (after heating) - T2 is the final temperature of the gas (after heating)

In this case, we know that the final temperature (T2) is 80 K and the final pressure (P2) is 20% higher than the initial pressure (P1). Let's denote the initial pressure as P1 and the final pressure as P2.

According to the problem, the final pressure (P2) is 20% higher than the initial pressure (P1). Mathematically, it can be represented as:

P2 = P1 + 0.2 * P1

Simplifying the equation, we get:

P2 = 1.2 * P1

Now, we can substitute the values of P2 and T2 into the ideal gas law equation:

(1.2 * P1) / T1 = P2 / T2

Simplifying further, we get:

1.2 * P1 / T1 = P1 / 80

Cross-multiplying the equation, we get:

1.2 * P1 * 80 = P1 * T1

Simplifying, we get:

96 * P1 = P1 * T1

Dividing both sides of the equation by P1, we get:

96 = T1

Therefore, the initial temperature of the gas is 96 K.

Answer

The initial temperature of the gas is 96 K.