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One gram molecule of oxygen is heated at constant pressure from 0°C. What amount of heat should be imparted to the gas to double it's volume? Given cp = 0.218 cal g-1 0 C-1. Class +1 ( Physics ) |
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Answer» ʏᴇs ᴏғᴄᴏᴜʀsᴇ ɪ ᴄᴀɴ ʙᴇ ᴜʀ ғʀɴᴅᴍʏsᴇʟғ ɢᴀʀɢɪ ᴄʟᴀss 7 ғʀᴏᴍ ᴍᴀʜᴀʀᴀsʜᴛʀᴀ ᴜʀs ɪɴᴛʀᴏ ᴘʟᴇᴀsᴇ? Explanation:Given info : one gram molecule of oxygen is heated at constant pressure from 0° C.To find : what amount of heat should be IMPARTED to the had to double its volume ?solution : one gram molecule means one mole.so no of moles of oxygen gas , n = 1work done , W = \int\limits^{2V}_{V}{P}\,dV V∫2V pdV = PV = nRT₀ = 1 × R T₀ = RT₀internal energy change, ∆U = \int\limits^{2V}_{V}C_vdT V∫2V C v dT= \int\limits^{2V}_V{\frac{R}{\gamma-1}}\,dT V∫2V γ−1R dTwe know, pdV = nRdTso, \int\limits^{2V}_V{\frac{P}{\gamma-1}}\,dV V∫2V γ−1P dV= \frac{pV}{\gamma-1}=\frac{RT_0}{\gamma-1} γ−1pV = γ−1RT 0 now from 1st LAW of thermodynamics,Q = W + ∆U⇒Q = RT₀ + RT₀/(γ - 1)for oxygen (diatomic molecule),γ = 1.4= 25/3 × 273 + 25/3 × 273/(1.4 - 1) J= 2275 + 2275/0.4= 2275 + 5687.5= 7962.5 JTherefore heat required to the gas to double its volume is 7962.5 Jʜᴏᴘᴇ ᴛʜɪs ᴡɪʟʟ ʜᴇʟᴘ ᴜ ᴅᴇᴀʀ.. |
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