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:
[tex]\boxed{\boxed{ \ \frac{pV}{T} = constant \ }}[/tex]
- p = pressure (in Pa)
- V = volume (in m³)
- T = temperature (in Kelvin)
The equations for state-1 and state-2 are as follows:
[tex]\boxed{ \ \frac{p_2V_2}{T_2} = \frac{p_1V_1}{T_1} \ }[/tex]
Conditions:
- p₂ = 2p₁
- We assume that the volume is constant, V₂ = V₁.
Let us calculate the final temperature T₂.
[tex]\boxed{ \ \frac{2p_1}{T_2} = \frac{p_1}{T_1} \ }[/tex]
[tex]\boxed{ \ \frac{2}{T_2} = \frac{1}{T_1} \ }[/tex]
T₂ x 1 = 2 x T₁
Thus, the temperature would we need to heat the gas to double its pressure is [tex]\boxed{ \ T_2 = 2T_1 \ }[/tex]
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Notes:
[tex]\boxed{ \ \frac{pV}{nT} = R \ } \rightarrow \boxed{ \ pV = nRT \ }[/tex]
n = moles of ideal gas
R = the molar gas constant (in J mol⁻¹ K⁻¹)
Learn more
- The energy density of the stored energy https://brainly.com/question/9617400
- Conservation of mass https://brainly.com/question/9473007
- The molality and mole fraction of water https://brainly.com/question/10861444
Keywords: an ideal gas, an absolute temperature, to heat the gas to double its pressure, volume, constant, moles, equation of state
