Chemistry

Question $2$

You are an engineer in a manufacturing plant. Your company will procure an important equipment that will contain and heat $100$ moles of ammonia gas. The initial condition of the ammonia gas will be at $15$ atm and $300$ liters. The ammonia gas will then be heated until it expands to $500$ liters while maintaining the $15$ atm pressure.

For this, a meeting with the accounting department is to be facilitated to talk about the cost of the said equipment.

A teammate of yours, an engineer and a previous classmate of yours, made his$/$her computations regarding the cost. You've found out that his$/$her computations are "ideal" that:

$(1)$ he$/$she used specific heat capacities intended only for $25\backslash$deg C and $100$ kpa conditions and $(2)$ he$/$she used ideal gas law.

From your extensive training in engineering school, you know that $(1)$ specific heat capacity varies with temperature and $(2)$ instead of using ideal gas law, it is more realistic to use real gas law" such as Van Der Waals equation $($see presented formula$).$

According to a research made by the RnD $($Research and Development$)$ department of your company, for every positive increase in the change of entropy in the process $($of the equipment to be procured$),$ the cost accounts for $300\mathrm{.}00$ Php$.$ Thus, $1$ J$/$K increase in entropy in the process of the said equipment corresponds to $300\mathrm{.}00$ Php; and $2/$K increase corresponds to $600\mathrm{.}00$ Php$.$

Save your workmate from his$/$her impending trouble by showing him$/$her the difference between the cost he$/$she computed $($ideal$)$ and yours $($realistic$)$ in Php$.$

Should your workmate present his$/$her computations, the accounting department will process the release of the financing of the equipment $($which could take some time $-$ profitability reviews, signatories of various bosses, etc.$).$ Once the money is released, it would be a lot trouble if what he$/$she requested is way below what it is supposed to be$.$

For the Van Der Waal's equation:

P $=$ atm

n $=$ mol

V $=$ L

T $=$ K

For ammonia with respect to the Van Der Waal's equation:

a $=4\mathrm{.}225$ L$^2/$mol$^2$

b $=0\mathrm{.}03713$ L$/$mol

Formula to convert Celsius to Kelvin is given by:

K$=\backslash$deg C$+273\mathrm{.}15$

Answer Format: $[2$ decimals$]$