IB MAI HL Calculus Topic 5.4 Differential Equations (id: 0287240ca)

本题目来源于试卷: IB MAI HL Calculus Topic 5.4 Differential Equations，类别为 IB数学

[填空题]
An experiment is conducted on a g *(pc3e,w7g :t/82h/ mrfpwvm jewhsqa6 g p+ib. zg:qwt2d;8u9evv kvs confined in a container. The pressure P measured in Pascals, and the volume +gvvt8pv e6 2;gbdwu.z: q9ki V measured in \mathrm{cm}^{3} satisfy the differential equation

$\frac{\mathrm{d}P}{\mathrm{d}V}=-\frac{P}{V}$


Initially, the gas has a pressure of 20000 Pascals and it is confined in a container with a volume of 100 ${\mathrm{cm}}^3$ .
1. Solve the differential equation to show that

P=$\frac{2000000}{V}$

2. Calculate the pressure required to compress the gas to a different container that has a volume of 50 ${\mathrm{cm}}^3$ .
P=   Pa.

参考答案: 40000


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