a$.2\mathrm{.}5$ kg of liquid water initially at $15$C is to be heated to $95$C in a teapot equipped with a $1200$ W electric heating element inside. The specific heat of water can be taken to be $4\mathrm{.}18$ kJ$/$kg$.$C$,$ and the heat loss from the water during heating can be neglected. The time it takes to heat the water to the desired temperature is:

$($a$)4\mathrm{.}6$ min $($b$)5\mathrm{.}6$ min $($c$)6\mathrm{.}7$ min $($d$)9\mathrm{.}0$ min $($e$)11\mathrm{.}6$ min

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b$.$ A $500-$m$3$ rigid tank is filled with saturated liquid$-$vapor mixture of water at $200$ kPa. If $11\%$ of the mass is liquid and the $89\%$ of the mass is vapor, the total mass in the tank is:

$($a$)705$ kg $($b$)500$ kg $($c$)258$ kg $($d$)635$ kg $($e$)2809$ kg

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c$.$ A $2-$m$3$ rigid tank contains nitrogen gas at $500$ kPa and $300$ K$.$ Now the gas is compressed isothermally to a volume of $0\mathrm{.}773$ m$3.$ The work done on the gas during this compression process is:

$($a$)950$ kJ $($b$)0$ kJ $($c$)1610$ kJ $($d$)2996$ kJ $($e$)562$ kJ