Question

a). Consider an ideal gas with an absolute temperature of T1. To what temperature would you need to heat the gas to double its pressure? Express your answer in terms of T1.

Answer 1

For an ideal gas, we use the ideal gas equation to relate pressure, volume and temperature changes. It is expressed as:

PV=nRT

For this case, we set V, n as constant. 

P/T = nR/V = constant = k
P = kT

P1/T1 = P2/T2
P1/T1 = 2P1 / T2
T2 = 2P1(T1) / P1
T2 = 2T1

Therefore, in order to double the pressure of the system, we need to double the temperature as well at constant volume and number of moles.

Answer 2

2T₁

Further explanation

Given:

An ideal gas with an absolute temperature of T₁.

Question:

To what temperature would you need to heat the gas to double its pressure?

The Process:

We use an equation of state for an ideal gas:

$\boxed{\boxed{ \ \frac{pV}{T} = constant \ }}$

• p = pressure (in Pa)
• V = volume (in m³)
• T = temperature (in Kelvin)

The equations for state-1 and state-2 are as follows:

$\boxed{ \ \frac{p_2V_2}{T_2} = \frac{p_1V_1}{T_1} \ }$

Conditions:

• p₂ = 2p₁
• We assume that the volume is constant, V₂ = V₁.

Let us calculate the final temperature T₂.

$\boxed{ \ \frac{2p_1}{T_2} = \frac{p_1}{T_1} \ }$

$\boxed{ \ \frac{2}{T_2} = \frac{1}{T_1} \ }$

T₂ x 1 = 2 x T₁

Thus, the temperature would we need to heat the gas to double its pressure is $\boxed{ \ T_2 = 2T_1 \ }$

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Notes:

$\boxed{ \ \frac{pV}{nT} = R \ } \rightarrow \boxed{ \ pV = nRT \ }$

n = moles of ideal gas

R = the molar gas constant (in J mol⁻¹ K⁻¹)

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Keywords: an ideal gas, an absolute temperature, to heat the gas to double its pressure, volume, constant, moles, equation of state