Free Printable CHEE2015 - Math Preliminaries

1.

A partial differential equation has:

a)

one independent variable.

b)

equal number of dependent and independent variables.

c)

more than one dependent variable.

d)

two or more independent variables

2.

If z is a function which depends on variables x and y, the change of z with respect to one of its variables is called as:

a)

Total derivative.

b)

Partial derivative.

c)

Inexact differential.

d)

I don't know :)

3.

If z is a function which depends on variables x and y, the change of z with respect to variable x can be expressed as

a)

$\left(\frac{\partial z}{\partial x}\right)_y$

b)

$\left(\frac{\partial z}{\partial x}\right)_x$

c)

$\left(\frac{\partial x}{\partial z}\right)_x$

d)

I don't know :)

4.

If z = f (x, y) ; then its total differential can be expressed as

a)

$dz=\left(\frac{\partial z}{\partial x}\right)_ydx\ +\left(\frac{\partial z}{\partial y}\right)_xdy$

b)

$dz=\left(\frac{\partial z}{\partial x}\right)_ydy\ +\left(\frac{\partial z}{\partial y}\right)_xdx$

c)

$dz=\left(\frac{\partial z}{\partial x}\right)_y\ +\left(\frac{\partial z}{\partial y}\right)_x\$

d)

$dz=\left(\frac{\partial z}{\partial x}\right)_x\ +\left(\frac{\partial z}{\partial y}\right)_y\$

5.

Molar volume is a function of temperature and the pressure or V = f (T, P) ; and its total derivative can be written as

a)

$dV=\left(\frac{\partial V}{\partial T}\right)_PdP+\left(\frac{\partial V}{\partial P}\right)_TdT$

b)

$dV=\left(\frac{\partial V}{\partial T}\right)_PdT+\left(\frac{\partial V}{\partial P}\right)_TdP$

c)

$dV=\left(\frac{\partial P}{\partial T}\right)_VdT+\left(\frac{\partial P}{\partial V}\right)_TdV$

d)

I don't know, I'm still confused!

6.

For an ideal gas, find explicit expression for the partial derivative: $\left(\frac{\partial V}{\partial T}\right)_{_P}$

a)

$\frac{RT}{P}$

b)

$\frac{P}{R}$

c)

$\frac{R}{P}$

d)

$\frac{T}{P}$

7.

For an ideal gas, find explicit expression for the partial derivative: $\left(\frac{\partial T}{\partial P}\right)_V$

a)

$\frac{V}{R}$

b)

$-\frac{RT}{V^2}$

c)

$\frac{P}{R}$

d)

$-\frac{RT}{P^2}$

8.

For an ideal gas, find explicit expression for the partial derivative: $\left(\frac{\partial P}{\partial V}\right)_T$

a)

$\frac{R}{V}$

b)

$\frac{R}{P}$

c)

$-\frac{RT}{P^2}$

d)

$-\frac{RT}{V^2}$

9.

For an ideal gas, evaluate the product of partial derivatives: $\left(\frac{\partial P}{\partial T}\right)_V\left(\frac{\partial T}{\partial V}\right)_P$

a)

$\frac{R^2}{PV}$

b)

$\frac{P}{V}$

c)

1

d)

$\frac{V}{P}$

10.

For an ideal gas, evaluate the product of partial derivatives:

\left(\frac{\partial P}{\partial V}\right)_T\left(\frac{\partial T}{\partial P}\right)_V\left(\frac{\partial V}{\partial T}\right)_P

a)

1

b)

-1

c)

R

d)

None of them

CHEE2015 - Math Preliminaries

Total questions: 10

Worksheet time: 9mins

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