Chapter 15. Work done by an ideal gas in an isothermal (constant-temperature) process (15-6)

Question

43IYlDwrsOm53LhVsMsrDN7eGbBuBRmy5qTbgg==
{"title":"Number of moles of gas","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Question

rBXFI7ACHUe0savIHOdfpP2t3o/Pmbaf
{"title":"Number of moles of gas","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Question

NuEvXKNXEN24RZJ4tEhDQ5+ZdDFInVwhIzMkCOw68boXcpVldCSSVpXT4CcscNkw
{"title":"Number of moles of gas","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Question

k+wougS0P4CghgaDjAqVfBkzPq8ZfBmAq42YMKynBGTvldhWP07xgWZUptpGqKM4s22UwMq5va8=
{"title":"Number of moles of gas","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Question

RQ0HLuRRl2XZW3ysZUJML3Yq2IWCkWFRO1c+CUkL2+RTGuCn
{"title":"Number of moles of gas","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Question

B6DEkr9l3ufvrqFyViNEtL7shO6Z49WQBR1jK6bOGZAx9zU1LuO8bCVTgoYUqCDPClFi178HDhw=
{"title":"Number of moles of gas","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"rect\",\"coords\":\"96,48,128,75\"}]"} {"title":"Ideal gas constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"124,35,157,75\"}]"} {"title":"Volume of the gas at the end of the process","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"250,0,298,55\"}]"} {"title":"Volume of the gas at the beginning of the process","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"251,65,298,116\"}]"} {"title":"Kelvin temperature of the gas","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"158,35,193,75\"}]"} {"title":"Work that an ideal gas does in an isothermal process","description":"Correct!","type":"correct","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"5,35,54,75\"}]"}

Review

On a \(pV\) diagram, the area under the curve represents the work \(W\) done by the gas; Figure 15-7b shows this area for an isothermal expansion. Unlike the isobaric case shown in Figure 15-6, the area under the curve is not a rectangle, so we cannot find \(W\) simply by multiplying the pressure and the change in volume. Using calculus, it can be shown that the work that the gas does as the volume changes is